Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×C32×#67 |
| Fitting | C25×C33 ⋊ C2 |
| Sylow | C33 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C32 | C2×D3 |
| commutator, cosocle | C2×C3 | C25×C32 |
| Frattini | C2 | C24×C32×D3 |
| Fitting | C25×C33 | C2 |
| socle | C24×C33 | C22 |
| hypercenter | C25×C32 | D3 |
| hypocenter | C3 | C23×C32×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C24×C32 ◁ C25×C32 | |
11164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
648 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×C3×((C22⋊C9)⋊C2)⋊C3, C2×#67×#1094 |
| maximal normal subgroup of | C2×#67×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47792);